CN114537517A - Adaptive reverse control method for steer-by-wire system for improving operation stability - Google Patents

Adaptive reverse control method for steer-by-wire system for improving operation stability Download PDF

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CN114537517A
CN114537517A CN202210281840.4A CN202210281840A CN114537517A CN 114537517 A CN114537517 A CN 114537517A CN 202210281840 A CN202210281840 A CN 202210281840A CN 114537517 A CN114537517 A CN 114537517A
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vehicle
steering
angle
steer
adaptive
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CN114537517B (en
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张旭
王东斌
王印
卢威
田栋
麻新兵
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Shaanxi Automobile Group Co Ltd
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B62—LAND VEHICLES FOR TRAVELLING OTHERWISE THAN ON RAILS
    • B62D—MOTOR VEHICLES; TRAILERS
    • B62D6/00—Arrangements for automatically controlling steering depending on driving conditions sensed and responded to, e.g. control circuits
    • B62D6/008—Control of feed-back to the steering input member, e.g. simulating road feel in steer-by-wire applications
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
    • Y02T90/00—Enabling technologies or technologies with a potential or indirect contribution to GHG emissions mitigation

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  • Combustion & Propulsion (AREA)
  • Transportation (AREA)
  • Mechanical Engineering (AREA)
  • Steering Control In Accordance With Driving Conditions (AREA)

Abstract

The invention discloses a steer-by-wire system adaptive backstepping control method for improving operation stability, which comprises the steps of 1, establishing a steering system model; step 2, designing a reference model system; step 3, designing a self-adaptive reverse pushing controller based on the ideal transmission ratio, which specifically comprises the following steps: step 31: is provided with
Figure 632746DEST_PATH_IMAGE001
Is the front wheel steering angle of the vehicle
Figure 278622DEST_PATH_IMAGE002
Relative vehicle responseyThe steering gain of (a) is obtained,
Figure 373617DEST_PATH_IMAGE003
is the steering wheel angle
Figure 88632DEST_PATH_IMAGE004
Relative vehicle responseyTo obtain an ideal front wheel steering angle input for the entire vehicle system
Figure 661696DEST_PATH_IMAGE005
(ii) a Step 32: ensuring vehicle yaw rate through virtual controlrStable in a certain area; step 33: designing the actual active control moment
Figure 83450DEST_PATH_IMAGE006
(ii) a Step 34: and verifying the dynamic stability of the system.

Description

Adaptive reverse control method for steer-by-wire system for improving operation stability
Technical Field
The invention belongs to the technical field of improving vehicle stability and self-adaptive control, and particularly relates to a self-adaptive reverse control method for a steer-by-wire system for improving operating stability.
Background
The steer-by-wire system cancels partial mechanical connection of the traditional steering system, so the steer-by-wire system ensures that the steering angle instruction input by the driver can be accurately transmitted to the front wheel to realize the normal rotation of the wheel, the design of the angle transmission characteristic is the key point of the steer-by-wire system, the steering sensitivity is unchanged through the design of the ideal steering transmission ratio, and the burden of the driver is further lightened, the ideal transmission ratio is the steering transmission ratio which can ensure that the gain of the steering wheel steering angle input relative to the automobile response is unchanged. At present, the ideal transmission ratio of the steer-by-wire system is mainly designed according to the unchanged steering gain, and the ideal transmission ratio design can realize easy steering and can keep the sensitivity of the vehicle during steering. In the design of a steering control system, the steering wheel angle is used as system input, and an ideal transmission ratio design is introduced, so that an ideal front wheel steering angle can be obtained, and powerful guarantee is provided for the accuracy of the steering performance analysis.
The steering stability performance is an important index for evaluating the quality of a steering system, and the vehicle has good steering stability, so that the comfort of drivers and passengers of the vehicle can be improved, and the safety of the vehicle can also be ensured. If the vehicle can not provide stable control of the lateral force and the yaw force, the vehicle body can generate irregular and uncertain lateral force and yaw movement, and the safety of drivers and passengers is seriously influenced. However, how to effectively control the stability control performance of the vehicle in the turning process, many researchers at home and abroad develop intensive research on the stability control performance, and the stability control performance of the whole vehicle is improved by introducing different control strategies.
Although the control described above has made great progress in improving vehicle performance, there are still some problems to be noted, on one hand, in designing the controller, the driving state and the authenticity of the actual vehicle are considered, the control target should not be set to the "zero" reference model, such design is too ideal, the developability and the practicability of the controller are low, and in order to consider the use value of the controller, in designing the controller, a nearly real ideal reference model should be introduced as the tracking target of the controller, so that the designed controller is easier to be manufactured in actual production. On the other hand, in the design of the whole vehicle stability control model, when accurate system modeling is considered, model uncertainty caused by different factors is ubiquitous, and therefore certain difficulty can be brought to the design and implementation of a control scheme, and therefore certain engineering practice significance is achieved when the uncertainty of the whole vehicle system model is considered.
The self-adaptive recursion control method is a preferred method of an uncertain system, and the principle of the method is a reverse recursion control method designed by combining a Lyapunov function, a state variable is selected as virtual control of a certain subsystem in a controlled system, the virtual control is required to enable the subsystem to be stable, meanwhile, the Lyapunov function is constructed and the system stability is proved, the self-adaptive recursion method can effectively realize self-adaptive adjustment on the system, and can carry out real-time adjustment and reasonable control according to different external conditions, so that the overall performance of the controlled system is improved.
However, the initial value setting range of the controlled system of the current research method is small, the control method has higher conservatism, and the controller mostly takes a zero reference curve as a control target, so that the control is over-ideal.
Disclosure of Invention
The invention aims to provide a self-adaptive reverse control method of a steer-by-wire system for improving the steering performance, which can solve the problem that the existing vehicle generates lateral deviation and yaw movement to the safety of drivers and passengers in the turning process, and solve the problems that a controller is subjected to yaw rotation inertia uncertainty, external interference and the like, the dynamic stability of a model and the like under the actual vehicle driving condition, realize the effective control of a whole vehicle system, and effectively improve the safety of the drivers and passengers and the steering stability of the vehicle.
In order to solve the problems in the prior art, the invention adopts the technical scheme that:
a steer-by-wire system self-adaptive backstepping control method for improving operation stability comprises the following steps:
step 1, establishing a steering system model.
And 2, designing a reference model system.
Step 3, designing a self-adaptive reverse pushing controller based on the ideal transmission ratio, and specifically comprising the following steps:
step 31: the steering gain of the front wheel steering angle of the vehicle relative to the vehicle response and the steering gain of the steering wheel steering angle relative to the vehicle response are set.
Step 32: and considering the uncertain parameters into a steering system model, and simultaneously using the yaw rate of the vehicle as a virtual control variable, and ensuring the stability of the yaw rate of the vehicle through virtual control.
Step 33: designing an actual active control moment to enable a dynamic error to approach zero or be bounded; an adaptive control law is defined.
Step 34: and verifying the dynamic stability of the system.
Further, in step 1, when the vehicle is turned, the vehicle body may generate lateral deviation and yaw motion, and the dynamic equation of the steering system obtained according to the model is as follows:
Figure 419552DEST_PATH_IMAGE001
in the formula (1)mIn order to be the mass of the vehicle body,I zexpressed as a yaw moment of inertia,Vin order to determine the speed at which the vehicle is operating,F yf andF yr respectively representing the lateral force of the front wheel and the rear wheel;βrepresenting a vehicle body slip angle;l f andl r representing the distance of the center of mass to the front and rear wheels, respectively. Yaw rate
Figure 887443DEST_PATH_IMAGE002
As state variables of the kinetic equation;M zrepresenting an actuator active cornering moment, wherein:
Figure 264197DEST_PATH_IMAGE003
in the formula (2)
Figure 9299DEST_PATH_IMAGE004
In the case of a small slip angle, the nonlinear tire lateral force can be approximated as shown in equation (2) using a small angle approximation:
Figure 587042DEST_PATH_IMAGE005
α f ，α r respectively, front and rear wheel side slip angles.θ vf ，θ vr Respectively the angle between the vehicle speed vector and the longitudinal axis of the vehicle. Tire slip angle refers to the angle between the tire plane and the velocity vector.
Substituting the formulas (2) to (3) into the formula (1):
Figure 417595DEST_PATH_IMAGE006
for convenience, equation (4) is rewritten as:
Figure 598041DEST_PATH_IMAGE007
wherein:
Figure 322283DEST_PATH_IMAGE008
meanwhile, state variables defining the steering system are as follows:
Figure 929982DEST_PATH_IMAGE009
conversion of kinetic equation (1) to
Figure 247831DEST_PATH_IMAGE010
In the formula (6)x 1Which represents the angle of the vehicle's yaw,x 2which represents the yaw angle of the vehicle,x 3which is indicative of the vehicle's cornering angular velocity,x 4the yaw rate is shown.
Further, in step 2, the reference system provides the yaw angle and the yaw rate of the vehicle body, so as to provide an ideal reference index for the controller, and ensure two control targets: the first aim is to control the yaw angle and the yaw angle to be stable; the second goal is to accurately track the reference model in real time according to the yaw angle and the yaw angle of the controlled model. The specific introduction method of the reference model comprises the following steps:
based on the nonlinear and uncertain system models of the actual vehicle, establishing a transfer function relation between a new slip angle and a reference model, and rewriting the slip angle as follows:
Figure 372913DEST_PATH_IMAGE011
wherein:
Figure 827028DEST_PATH_IMAGE012
k z is an adjustable parameter, and meanwhile, the virtual control input can be ensured by the formula (8)
Figure 871207DEST_PATH_IMAGE013
Converge to a desired yaw rate
Figure 676352DEST_PATH_IMAGE014
The ideal lateral deviation angle under the reference model can be obtained by the formula (8) and the formula (9)
Figure 588814DEST_PATH_IMAGE015
And yaw rate
Figure 897435DEST_PATH_IMAGE016
The invention selects the steady state
Figure 112516DEST_PATH_IMAGE015
And yaw rate
Figure 277393DEST_PATH_IMAGE016
Is a reference curve.
Further, the step 31 specifically includes: in order to obtain ideal input of a controlled whole vehicle system, it is necessary to design an ideal transmission ratio, and the ideal transmission ratio in the steer-by-wire system is designed by switching the steering characteristics from the steering wheel angle to the front wheel angle, so as to ensure the steering sensitivity of the vehicle and set
Figure 603333DEST_PATH_IMAGE017
Is the front wheel steering angle of the vehicle
Figure 32040DEST_PATH_IMAGE018
Relative vehicle responseyThe steering gain of (a) is obtained,
Figure 542656DEST_PATH_IMAGE019
is the steering wheel angle
Figure 56814DEST_PATH_IMAGE020
Relative vehicle responseySteering gain of (1).
Figure 186444DEST_PATH_IMAGE021
Defined again according to the transmission ratio:
Figure 735237DEST_PATH_IMAGE022
further obtaining:
Figure 167486DEST_PATH_IMAGE023
step 32: in real life, the invention will change the cornering inertia when turning with the change of the number of passengers and the load of the vehicleI zSelected as the uncertainty parameter of the system. Since the moment of inertia varies within a certain range, it is assumed thatI zIs bounded by
Figure 168940DEST_PATH_IMAGE024
Simultaneously order
Figure 102261DEST_PATH_IMAGE025
。Taking uncertain parameters into account in a steering system while simultaneously taking yaw rate of a vehicle into accountrEnsuring the yaw rate of a vehicle by virtual control as a virtual control variablerIs stable in a certain area.
As can be seen from the formula (7)
Figure 364615DEST_PATH_IMAGE026
Selecting the actual virtual control function as
Figure 92400DEST_PATH_IMAGE027
Design desired value of virtual control
Figure 581150DEST_PATH_IMAGE028
So that only the yaw rate is required
Figure 52583DEST_PATH_IMAGE029
Can make the vehicle offset laterally
Figure 185755DEST_PATH_IMAGE030
Trend to reference model
Figure 350020DEST_PATH_IMAGE031
Stabilized and satisfied, and defined
Figure 326066DEST_PATH_IMAGE032
As vehicle cornering angle
Figure 335610DEST_PATH_IMAGE030
And a reference model
Figure 838136DEST_PATH_IMAGE033
Error therebetween, i.e.
Figure 642144DEST_PATH_IMAGE034
Simultaneous definition of
Figure 105486DEST_PATH_IMAGE035
As actual state values
Figure 794088DEST_PATH_IMAGE036
And expected value
Figure 26486DEST_PATH_IMAGE028
Error therebetween, i.e.
Figure 532554DEST_PATH_IMAGE037
: defining a first bound Lyapunov candidate function
Figure 217613DEST_PATH_IMAGE038
Selecting a virtual control variable as a function of the Lyapunov candidate function (13)
Figure 959173DEST_PATH_IMAGE039
Wherein
Figure 46077DEST_PATH_IMAGE040
To paire 1(t) The derivation is carried out to obtain:
Figure 723046DEST_PATH_IMAGE041
by substituting formulae (12) to (13) into formula (14), it is possible to obtain:
Figure 895402DEST_PATH_IMAGE042
step 33: designing the actual active control moment
Figure 657297DEST_PATH_IMAGE043
Make a dynamic errore 2(t) Approaching zero or bounded; to paire 2(t) The derivation is carried out to obtain:
Figure 864287DEST_PATH_IMAGE044
in equation (19):k 2is a constant number of times, and is,
Figure 712158DEST_PATH_IMAGE045
is that
Figure 496443DEST_PATH_IMAGE046
An estimated value of (d);
next, an adaptive control law is defined:
Figure 455172DEST_PATH_IMAGE047
in formula (17)
Figure 251089DEST_PATH_IMAGE048
And is a constant, which is an adaptive control law adjustable parameter.
Step 34: verifying system dynamic stability
Selecting a half positive definite limit Lyapunov candidate function:
Figure 879648DEST_PATH_IMAGE049
derivation of equation (21) and substitution of equations (17) - (19) can yield:
Figure 26595DEST_PATH_IMAGE050
according to the nature of projection theorem
Figure 789015DEST_PATH_IMAGE051
Is obtained by
Figure 705018DEST_PATH_IMAGE052
Derivation of equation (23)
Figure 753746DEST_PATH_IMAGE053
Due to the fact that
Figure 387990DEST_PATH_IMAGE054
Is consistent and continuous and satisfies when
Figure 688521DEST_PATH_IMAGE055
When the temperature of the water is higher than the set temperature,
Figure 334397DEST_PATH_IMAGE056
(ii) a Thus, it is possible to obtain
Figure 429392DEST_PATH_IMAGE057
Trace error
Figure 550932DEST_PATH_IMAGE058
Gradually stabilizes, and the system reaches a steady state.
Further, the method also comprises a step 4 of selecting proper gaink 1，k 2And
Figure 655154DEST_PATH_IMAGE059
therefore, all constraints can be limited within a reasonable range under the interference of uncertain parameters in the system, the control target is achieved, and the control requirement is met.
The invention has the following beneficial effects:
1) the invention takes the real track of the actual vehicle as the target, introduces an ideal system model to obtain the ideal control target of the yaw angle and the yaw angle, and lays the foundation for the tamping for verifying the effectiveness of the invention.
2) The invention introduces an ideal angle transmission ratio design, keeps the steering sensitivity of the steer-by-wire system, and provides ideal front wheel steering angle input for an analysis control system.
3) According to the method, the self-adaptive adjustment control law is designed based on the limit Lyapunov function aiming at the uncertainty of the yaw moment of inertia in the controlled system model, the online estimation of the uncertain parameters of the model is realized, the influence of the uncertain parameters on the controlled system is adjusted, the yaw and the lateral movement of the vehicle are stabilized, and the operation stability performance of the vehicle is effectively improved.
4) The selected limit Lyapunov function has lower conservative property than a secondary Lyapunov function, and the initial value selection range of the controlled system is larger.
5) The invention considers the tracking performance of the controller, designs virtual control to eliminate tracking error and obtains corresponding active control moment, so that the vehicle can still well track the preset control target under different speeds and different turning road conditions.
6) The control method can be used for popularization, can be combined with other controller designs, is easy to realize, does not need redundant hardware in a system, and is low in cost.
Drawings
FIG. 1 is a two-degree-of-freedom system model of a whole vehicle in the invention.
Fig. 2 is a control schematic diagram of the present invention.
Fig. 3 is a plot of ideal gear ratio versus front wheel steering angle for the present invention.
Fig. 4 is a plot of yaw angle versus angular velocity for a passive-by-wire steering system versus an active-by-wire steering system.
FIG. 5 is a plot of yaw angle versus angular velocity for a passive-by-wire steering system versus an active-by-wire steering system.
Fig. 6 is a yaw angle error tracking curve and a yaw angle error tracking curve.
Detailed Description
The invention will be further elucidated with reference to the drawings and reference numerals.
In order that the above objects, features and advantages of the present invention can be more clearly understood, a detailed description of the present invention will be given below with reference to the accompanying drawings and specific embodiments. It should be noted that the embodiments and features of the embodiments of the present application may be combined with each other without conflict.
The terms "first," "second," "third," and the like are used solely to distinguish one from another and are not to be construed as indicating or implying relative importance.
In the description of the present invention, it should also be noted that, unless otherwise explicitly specified or limited, the terms "disposed," "mounted," "connected," and "connected" are to be construed broadly and may, for example, be fixedly connected, detachably connected, or integrally connected; can be mechanically or electrically connected; they may be connected directly or indirectly through intervening media, or they may be interconnected between two elements. The specific meanings of the above terms in the present invention can be understood in specific cases to those skilled in the art.
The following detailed description of embodiments of the invention refers to the accompanying drawings. It should be understood that the detailed description and specific examples, while indicating the preferred embodiment of the invention, are given by way of illustration and explanation only, not limitation.
Example 1:
as shown in fig. 1 and 2, a steer-by-wire system adaptive back-thrust control method for improving operation stability includes the following steps:
step 1, establishing a steering system model, wherein when a vehicle turns, a vehicle body can generate lateral deviation and yaw movement, and the dynamic equation of the steering system obtained according to the model is as follows:
Figure 404804DEST_PATH_IMAGE060
in the formula (1)mIn order to be the mass of the vehicle body,I zexpressed as a yaw moment of inertia,Vin order to determine the speed at which the vehicle is operating,F yf andF yr respectively representing the lateral force of the front wheel and the rear wheel;βrepresenting a vehicle body slip angle;l f andl r representing the distance of the center of mass to the front and rear wheels, respectively. Yaw rate
Figure 670700DEST_PATH_IMAGE061
As state variables of the kinetic equation;M zrepresenting an actuator active cornering moment, wherein:
Figure 13957DEST_PATH_IMAGE062
in the formula (2)
Figure 797236DEST_PATH_IMAGE063
In the case of a small slip angle, the nonlinear tire lateral force can be approximated as shown in equation (2) using a small angle approximation:
Figure 542339DEST_PATH_IMAGE064
α f ，α r respectively, front and rear wheel side slip angles.θ vf ，θ vr Respectively the angle between the vehicle speed vector and the longitudinal axis of the vehicle. Tire slip angle refers to the angle between the tire plane and the velocity vector.
Substituting the formulas (2) to (3) into the formula (1):
Figure 244715DEST_PATH_IMAGE065
for convenience, equation (4) is rewritten as:
Figure 495175DEST_PATH_IMAGE066
wherein:
Figure 941200DEST_PATH_IMAGE067
meanwhile, state variables defining the steering system are as follows:
Figure 540808DEST_PATH_IMAGE009
conversion of kinetic equation (1) to
Figure 414086DEST_PATH_IMAGE068
In the formula (6)x 1Which represents the angle of the vehicle's yaw,x 2which represents the yaw angle of the vehicle,x 3which is indicative of the vehicle's cornering angular velocity,x 4the yaw rate is shown.
Step 2, designing a reference model system, wherein the reference system provides a yaw angle and a yaw velocity of the vehicle body, and aims to provide an ideal reference index for the controller and ensure control targets in two aspects: the first aim is to control the yaw angle and the yaw angle to be stable; the second goal is to accurately track the reference model in real time according to the yaw angle and the yaw angle of the controlled model. The specific introduction method of the reference model comprises the following steps:
based on the nonlinear and uncertain system models of the actual vehicle, establishing a transfer function relation between a new slip angle and a reference model, and rewriting the slip angle as follows:
Figure 856569DEST_PATH_IMAGE011
wherein:
Figure 840705DEST_PATH_IMAGE069
k z is an adjustable parameter, and meanwhile, the virtual control input can be ensured by the formula (8)
Figure 560400DEST_PATH_IMAGE070
Converge to a desired yaw rate
Figure 604579DEST_PATH_IMAGE014
The ideal lateral deviation angle under the reference model can be obtained by the formula (8) and the formula (9)
Figure 285090DEST_PATH_IMAGE071
And yaw rate
Figure 72918DEST_PATH_IMAGE072
The invention selects the steady state
Figure 647119DEST_PATH_IMAGE071
And yaw rate
Figure 862199DEST_PATH_IMAGE072
Is a reference curve.
Step 3, designing a self-adaptive reverse pushing controller based on the ideal transmission ratio, and specifically comprising the following steps:
step 31: in order to obtain ideal input of a controlled whole vehicle system, it is necessary to design an ideal transmission ratio, and the ideal transmission ratio in the steer-by-wire system is designed by switching the steering characteristics from the steering wheel angle to the front wheel angle, so as to ensure the steering sensitivity of the vehicle and set
Figure 13695DEST_PATH_IMAGE073
Is the front wheel steering angle of the vehicle
Figure 605213DEST_PATH_IMAGE074
Relative vehicle responseyThe steering gain of (a) is obtained,
Figure 768341DEST_PATH_IMAGE075
is the steering wheel angle
Figure 26760DEST_PATH_IMAGE076
Relative vehicle responseySteering gain of (1).
Figure 806497DEST_PATH_IMAGE077
Defined again according to the transmission ratio:
Figure 936127DEST_PATH_IMAGE078
further obtaining:
Figure 219341DEST_PATH_IMAGE079
through reasonable design of ideal transmission ratio, guarantee
Figure 166437DEST_PATH_IMAGE080
Is a constant. The invention determines the ideal transmission ratio of the steer-by-wire system by using a fuzzy control method, selects the triangular function which is most applied at present as the membership function of the fuzzy control, and selects the fuzzy functionControlling input vehicle speed and steering wheel angle, selecting vehicle speedVThe range of (a) is 0-150 km/h, i.e. the basic discourse area is [ 0150%]It is divided equally into 7 parts to form fuzzy set domains, which are expressed as {0, 25, 50, 75, 100, 125, 150 }; the translation to speech amount may be expressed as { NB, NM, NS, 0, PS, PM, PB }, and similarly, steering wheel angle
Figure 902312DEST_PATH_IMAGE081
The selection mode is the same as the vehicle speed, but the selection range is 0-720, so that the obtained basic domain is [ 0720 ]]The fuzzy set domain is {0, 120, 240, 360, 480, 600, 720 }; the translation to speech volume is also denoted as { NB, NM, NS, 0, PS, PM, PB }. The output is an ideal transmission ratio, the vehicle transmission ratio range is 6-24, and the fuzzy set domain is divided into 7 parts like the vehicle speed and the steering wheel, wherein the fuzzy set domain is {6, 9, 12, 15, 18, 21 and 24 }; the translation to speech volume is also denoted as { NB, NM, NS, 0, PS, PM, PB }. The design choice of the desired gear ratio utilizes the general sentence form of if A and B then C.
The invention uses the vehicle speedVAnd steering wheel angle
Figure 835633DEST_PATH_IMAGE081
The fuzzy controller with the ideal transmission ratio i as the output realizes the solution of the ideal transmission ratio for input, and the control strategy form is if V is A and
Figure 848719DEST_PATH_IMAGE081
the form of is B the is C, and finally according to the formula (11), the ideal front wheel steering angle input of the whole vehicle system is obtained
Figure 842083DEST_PATH_IMAGE082
。
Step 32: in real life, the invention will change the cornering inertia when turning with the change of the number of passengers and the load of the vehicleI zSelected as the uncertainty parameter of the system. Since the moment of inertia varies within a certain range, it is assumed thatI zIs bounded by
Figure 330833DEST_PATH_IMAGE083
Simultaneously order
Figure 661320DEST_PATH_IMAGE084
。Taking uncertain parameters into account in a steering system while simultaneously taking yaw rate of a vehicle into accountrEnsuring the yaw rate of a vehicle by virtual control as a virtual control variablerIs stable in a certain area.
As can be seen from the formula (7)
Figure 919126DEST_PATH_IMAGE085
Selecting the actual virtual control function as
Figure 83392DEST_PATH_IMAGE027
Design desired value of virtual control
Figure 403646DEST_PATH_IMAGE028
So that only the yaw rate is required
Figure 678769DEST_PATH_IMAGE029
Can make the vehicle offset laterally
Figure 56661DEST_PATH_IMAGE030
Trend to reference model
Figure 126248DEST_PATH_IMAGE031
Stabilized and satisfied, and defined
Figure 714224DEST_PATH_IMAGE032
As vehicle cornering angle
Figure 527459DEST_PATH_IMAGE030
And a reference model
Figure 494278DEST_PATH_IMAGE086
Error therebetween, i.e.
Figure 610133DEST_PATH_IMAGE087
Simultaneous definition of
Figure 560772DEST_PATH_IMAGE088
As actual state values
Figure 177698DEST_PATH_IMAGE089
And expected value
Figure 264602DEST_PATH_IMAGE028
Error therebetween, i.e.
Figure 66205DEST_PATH_IMAGE037
: defining a first bound Lyapunov candidate function
Figure 238560DEST_PATH_IMAGE090
Selecting a virtual control variable as follows from the Lyapunov candidate function equation (13)
Figure 128019DEST_PATH_IMAGE091
Wherein
Figure 207446DEST_PATH_IMAGE092
To paire 1(t) The derivation is carried out to obtain:
Figure 789737DEST_PATH_IMAGE093
by substituting formulae (12) to (13) into formula (14), it is possible to obtain:
Figure 449389DEST_PATH_IMAGE094
step 33: designing the actual active control moment
Figure 408117DEST_PATH_IMAGE095
So as to make dynamic errorse 2(t) Approaching zero or bounded; to paire 2(t) The derivation is carried out to obtain:
Figure 328669DEST_PATH_IMAGE096
in equation (19):k 2is a constant number of times, and is,
Figure 347440DEST_PATH_IMAGE097
is that
Figure 494388DEST_PATH_IMAGE098
An estimated value of (d);
next, an adaptive control law is defined:
Figure 866595DEST_PATH_IMAGE099
in formula (17)
Figure 782598DEST_PATH_IMAGE100
And is a constant, which is an adaptive control law adjustable parameter.
Step 34: verifying system dynamic stability
Selecting a half positive definite limit Lyapunov candidate function:
Figure 972271DEST_PATH_IMAGE101
derivation of equation (21) and substitution of equations (17) - (19) can yield:
Figure 465569DEST_PATH_IMAGE102
according to the nature of projection theorem
Figure 766100DEST_PATH_IMAGE103
Is obtained by
Figure 536610DEST_PATH_IMAGE052
Derivation of equation (23)
Figure 897184DEST_PATH_IMAGE052
Due to the fact that
Figure 894090DEST_PATH_IMAGE054
Is consistent and continuous and satisfies when
Figure 732733DEST_PATH_IMAGE104
When the temperature of the water is higher than the set temperature,
Figure 357750DEST_PATH_IMAGE056
. Thus, it is possible to obtain
Figure 13859DEST_PATH_IMAGE105
，
Figure 357116DEST_PATH_IMAGE106
Trace error
Figure 265029DEST_PATH_IMAGE058
Gradually stabilizes, and the system reaches a steady state.
Step 4, selecting proper gaink 1, k 2And
Figure 10131DEST_PATH_IMAGE107
therefore, all constraints can be limited within a reasonable range under the interference of uncertain parameters in the system, the control target is achieved, and the control requirement is met.
In step 34 of the present embodiment, according to equation (23), it can be concluded that:
Figure 587874DEST_PATH_IMAGE108
(ii) a Further obtain
Figure 418427DEST_PATH_IMAGE109
Therefore, it isIt is possible to obtain:
Figure 598872DEST_PATH_IMAGE110
it is thus known that the yaw angle and yaw rate of the vehicle are bounded, and the values of C1 and C2 within this bound may be infinitely small.
Example 2:
1-6, the description herein of the uncertainty in the moment of inertia of a steerable steering system is: moment of inertiaI z =1500-1700(kg)。
The present embodiment selects the vehicle speed of step 31v= (0-150 km/h) and steering wheel corner
Figure 464060DEST_PATH_IMAGE111
= (0-720 °) variable transmission ratioi=6 to 24, and according to the formula (11), a steering wheel angle can be further obtained
Figure 461972DEST_PATH_IMAGE111
In relation to the angle of rotation of the front wheel
Figure 779821DEST_PATH_IMAGE112
To verify the effectiveness of the present invention, two different steering wheel angle changes and vehicle speed changes (sin and cos) are given as inputs of a comprehensive feedback control strategy, and the expression is as follows:
Figure 763958DEST_PATH_IMAGE113
it should be noted that the vehicle speed and the steering wheel angle range selected by the research meet the conditions of normal driving, the universality and the universality are achieved, and the research on the stability performance of the whole vehicle and the sensitivity of the steer-by-wire is greatly facilitated.
Some actual vehicle steer-by-wire system parameter: the parameters of the automobile steer-by-wire system are the total mass of the automobile:m1880 kg; speed of vehicleV=20m/s, wheelbasel f =1m，l r =1.5 m. Coefficient of tyreμ=0.8, front tire modulus of elasticityC f = 20000N/m; coefficient of elasticity of rear wheel tireC r =20000N/m；
Selecting control law parameters: k 1=k 2= 10；
Figure 483652DEST_PATH_IMAGE114
=0.01; initial value condition of systemx i (0) =0cm (i=1,2,3,4), the lei apunov candidate function Δ = 0.08.
A two-degree-of-freedom steer-by-wire system model dynamic model is built in Simulink, a front wheel corner is solved based on Fuzzy, a self-adaptive back-pushing controller is built, time domain simulation is carried out on a controlled system by combining control parameters, and the built steer-by-wire system under the self-adaptive back-pushing control (called an active steer-by-wire system for short) is compared with a passive steer-by-wire system, so that the effectiveness of the controller is verified.
FIG. 3 is an ideal gear ratioiInputting a curve with the front wheel steering angle; fig. 4-5 are plots of yaw angle, angular velocity, angular acceleration versus yaw angle, angular velocity, angular acceleration for a passive-by-wire steering system versus an active-by-wire steering system. Fig. 6 is a yaw-rate error tracking curve.
It can be seen from fig. 3 that different gear ratio curves and different front wheel rotation angles can be obtained based on the Fuzzy technology when different steering wheel rotation angles and vehicle speeds are given, so as to provide different control inputs for the adaptive back-pushing controller, and better verify the quality of the controller.
The yaw motion and the yaw motion of the vehicle are both important indexes of vehicle operation stability and important indexes of evaluating the control performance of the controller, and as can be seen from the figures 4 to 5, under the condition of different front wheel corner control inputs (sin and cos), all curves of the active steer-by-wire system meet the requirement of the performance index of the vehicle operation stability, and have lower yaw and side inclination angle peak values compared with the passive steer-by-wire system, and simultaneously, the yaw, side inclination angle and angular velocity performance indexes of the drive-by-wire system are respectively improved (sin input) compared with the yaw, side inclination angle and angular velocity performance indexes of the passive steer-by-wire system): the yaw angle is 85.9 percent, the yaw rate is 88.3 percent, the yaw angle is 80.4 percent, and the yaw rate is 77 percent; (cos input): the yaw angle is 86.1%, the yaw rate is 80.5%, the yaw angle is 72.2%, and the yaw rate is 80%, so that the operation stability of the vehicle is effectively improved. As can be seen from the analysis of FIG. 6, the tracking error of the adaptive back-thrust controller is controlled to 10 regardless of the yaw-rate tracking curve or the yaw-angle tracking curve-3The controller provided by the invention can accurately track an ideal reference model, and meanwhile, the controller still has good tracking accuracy under the condition that the controlled system has uncertain parameters. When an actual vehicle runs, system parameters are continuously changed, and meanwhile, aiming at a steer-by-wire system, how to ensure that the steering sensitivity is unchanged puts forward higher requirements on the development of a controller. Therefore, the adaptive controller developed by the invention can greatly improve the operation stability of the steer-by-wire system. When the vehicle turns, if a high-quality controller is not developed, the steering sensitivity of the vehicle cannot be ensured, and the operating stability of the vehicle can be deteriorated.
The invention is not limited to the above alternative embodiments, and any other various forms of products can be obtained by anyone in the light of the present invention, but any changes in shape or structure thereof, which fall within the scope of the present invention as defined in the claims, fall within the scope of the present invention.

Claims (8)

1. A steer-by-wire system self-adaptive backstepping control method for improving operation stability is characterized by comprising the following steps:
step 1, establishing a steering system model;
step 2, designing a reference model system;
step 3, designing a self-adaptive reverse pushing controller based on the ideal transmission ratio, and specifically comprising the following steps:
step 31: setting a steering gain of a front wheel steering angle of the vehicle relative to the response of the vehicle, and setting a steering gain of a steering wheel steering angle relative to the response of the vehicle;
step 32: considering the uncertain parameters into a steering system model, simultaneously taking the yaw rate of the vehicle as a virtual control variable, and ensuring the stability of the yaw rate of the vehicle through virtual control;
step 33: designing an actual active control moment to enable a dynamic error to approach zero or be bounded; defining a self-adaptive control law;
step 34: and verifying the dynamic stability of the system.
2. The adaptive back-thrust control method of the steer-by-wire system for improving the steering performance according to claim 1, wherein: in the step 1, the dynamic equation of the steering system obtained according to the steering system model is as follows:
Figure DEST_PATH_IMAGE001
in the formula (7)mIn order to be the mass of the vehicle body,I zexpressed as a yaw moment of inertia,Vin order to determine the speed at which the vehicle is operating,F yf andF yr respectively representing the lateral force of the front wheel and the rear wheel;l f andl r respectively representing the distances of the center of mass to the front and rear wheels;M zrepresenting the active yawing moment, x, of the actuator1Indicating vehicle yaw angle, x2Representing vehicle yaw angle, x3Representing vehicle yaw rate, x4The yaw rate is shown.
3. The adaptive back-thrust control method of the steer-by-wire system for improving the steering performance according to claim 2, characterized in that: the step 2 specifically comprises the following steps: based on the nonlinear and uncertainty system models of the actual vehicle, establishing a transfer function relation between a new slip angle and a reference model:
Figure DEST_PATH_IMAGE002
wherein:
Figure DEST_PATH_IMAGE003
k z is an adjustable parameter, and meanwhile, the virtual control input can be ensured by the formula (8)
Figure DEST_PATH_IMAGE004
Converge to a desired yaw rate;
Figure DEST_PATH_IMAGE005
the ideal lateral deviation angle under the reference model can be obtained by the formula (8) and the formula (9)
Figure DEST_PATH_IMAGE006
And yaw rate
Figure DEST_PATH_IMAGE007
。
4. The adaptive back-thrust control method of the steer-by-wire system for improving the steering performance according to claim 3, wherein: the step 31 specifically includes: is provided with
Figure DEST_PATH_IMAGE008
Is the front wheel steering angle of the vehicle
Figure DEST_PATH_IMAGE009
Relative vehicle responseyThe steering gain of (a) is obtained,
Figure DEST_PATH_IMAGE010
is the steering wheel angle
Figure DEST_PATH_IMAGE011
Relative vehicle responseySteering gain of (2):
Figure DEST_PATH_IMAGE012
defined again according to the transmission ratio:
Figure DEST_PATH_IMAGE013
at the speed of the vehicleVAnd steering wheel angle
Figure DEST_PATH_IMAGE014
For input, the fuzzy controller with ideal transmission ratio i as output realizes the solution of the ideal transmission ratio, and finally obtains the ideal front wheel steering angle input of the whole vehicle system according to the formula (11)
Figure DEST_PATH_IMAGE015
。
5. The adaptive back-thrust control method of the steer-by-wire system for improving the steering performance according to claim 4, wherein: in the step 32: taking uncertain parameters into account in a steering system while simultaneously taking yaw rate of a vehicle into accountrEnsuring the yaw rate of a vehicle by virtual control as a virtual control variablerThe stability of (2);
selecting a virtual control variable, one can obtain:
Figure DEST_PATH_IMAGE016
wherein
Figure DEST_PATH_IMAGE017
To paire 1(t) The derivation is carried out to obtain:
Figure DEST_PATH_IMAGE018
。
6. the adaptive back-thrust control method of the steer-by-wire system for improving the steering performance according to claim 5, wherein: the step 33 is specifically: designing the actual active control moment
Figure DEST_PATH_IMAGE019
：
Figure DEST_PATH_IMAGE020
In equation (19):k 2is a constant number of times, and is,
Figure DEST_PATH_IMAGE021
is that
Figure DEST_PATH_IMAGE022
An estimated value of (d);
defining an adaptive control law:
Figure DEST_PATH_IMAGE023
in formula (17)
Figure DEST_PATH_IMAGE024
And is a constant, which is an adaptive control law adjustable parameter.
7. The adaptive back-thrust control method of the steer-by-wire system for improving the steering performance according to claim 6, wherein: said step 34 comprises: selecting a half positive definite limit Lyapunov candidate function;
from the projection theorem property, we can obtain:
Figure DEST_PATH_IMAGE025
wherein the content of the first and second substances,k 1、k 2is a constant;
Figure DEST_PATH_IMAGE026
is that
Figure DEST_PATH_IMAGE027
An estimated value of (d);
due to the fact that
Figure DEST_PATH_IMAGE028
Is consistent and continuous and satisfies when
Figure DEST_PATH_IMAGE029
When the temperature of the water is higher than the set temperature,
Figure DEST_PATH_IMAGE030
；
thus, it is possible to obtain
Figure DEST_PATH_IMAGE031
I.e. tracking error e1， e2Gradually stabilizes, and the system reaches a steady state.
8. The adaptive back-thrust control method of the steer-by-wire system for improving the steering performance according to claim 4, wherein: in the step 31, the range of the selected vehicle speed V is 0-150 km/h.
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